Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10623094 | C2 | semidirect |
| 2. C8×D4×C11 | C2 | semidirect |
| 3. #10622728 | C2 | semidirect |
| 4. #10622719 | C2 | semidirect |
| 5. #10622455 | C2 | semidirect |
| 6. #10622350 | C2 | semidirect |
| 7. C4×D88 | C2 | semidirect |
| 8. #10622295 | C2 | semidirect |
| 75. C8×D4 | D11 | semidirect |
| 136. C11 | #3341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623094 | 2 |
| C8×D4×C11 | 2 |
| #10622728 | 2 |
| #10622719 | 2 |
| #10622455 | 2 |
| #10622350 | 2 |
| C4×D88 | 2 |
| #10622295 | 2 |
| #3341 | 11 |